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[SOUND] Hello, in these lectures 14 and 15.

I'm going to describe to you, a number of case studies that

combine experiments and computational modeling to

understand complex behavior starting from literally

simple complex systems to more complex, complex systems.

in, in, in one case we will consider a

recent publication for whole cell model for a bacteria.

Okay let's get started.

The first study that I want to talk

to you about, is a circadian oscillator in bacteria.

Cyanobacterium like many other cells, have clock proteins.

And the clock protein here is called KaiC.

This is a protein that allows the

cyanobacterium to respond to light in dark cycles.

In KaiC, it has both intrinsic protein kinase, and protein

phosphatase activity, such that it

autoautophosphorylates itself, and also autodephosphorylates itself.

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KaiC is regulated by a protein called KaiA.

And KaiA, is stimulates the autophosphorylation of KaiC, and there is

a third protein in the system, KaiB which inhibits the effect of KaiA and KaiC.

So it sort of it's a modatory protein.

Shown bellow is the experiment done by the

Japanese group, Kondo's group who first discovered this.

And, you can see, that the phosphorylation

of KaiC follows this beautiful sort of rhythm.

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Rhythmic oscillations with a 24 hour cycle.

And this experiments was done with a

purified reconstituted system, which means that they

purified the three proteins, put them together,

added some ATP and other good stuff.

To allow the enzymatic reactions to proceed

and so the cyclical phosphorylation of KaiC.

This is kind of like a pretty

interesting and sort of, what shall I say, noteworthy observation,

because typically circadian rhythms involve transcription

and more complex transcriptional and translational regulation.

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However in this system we appear to be

purely driven by a enzymatic a few enzymatic reactions.

So the question is how does the simple

system of just three proteins produce sustained circadian oscillations.

The total [UNKNOWN] phosphorylation of KaiC

cannot be the only dynamic variable available.

Because in a 24-hour period, the KaiC protein

has the same level of phosphorylation at least twice.

And so, and but this level is reached going in opposite directions.

So how would the KaiC protein phospho KaiC know

which direction it should go in at any given time.

So there must be another variable that

contributes to this overall pattern of circadian oscillations.

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so, the Eleanor Oshay's group looked at this in some detail.

And what he found was that KaiC is phosphorylated on two sides.

Seating for 31 and training for 32.

And in that, two states are phosphorylated with the, the two sides.

The serine and the threonine, and, hence the two states of the protein.

Are phosphorylated with a 24 hour cycle, but they are phase separated.

And you can see this clearly when you look at the phosphorylation.

Of the [INAUDIBLE] site, which is in green.

And the [UNKNOWN] site, which is in red.

They're, You can see that they cycle differently.

They did the following experiments.

They showed that when KaiC, KaiA, is mixed with unphosphorylated KaiC.

KaiC is phosphorylated at [INAUDIBLE].

And then it dually phospholated, and then and only then does the [UNKNOWN] form.

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So essentially, what they found experimentally was that, for Kai, Saline

Kai31, for 31 KaiC, KaiA complex binds

KaiB leading to inhibition of KaiA, and stimulation of the activity.

The auto-phosphate, phosphate activity is unaffected by

chi b, and the system starts to cycle.

They could take these observations, and then build

a computational model for the KaiC circadian oscillator.

This the model that bears an ODE model, with three phosphorylated states.

The training phosphorylated T, the W, phosphorylated ST,

and the singally phosphorylated [UNKNOWN] state in new

meaning unphosphorylated We obtain the kinetic parameters

for the, the equations for these states given here.

We obtain the kinetic parameters for the model, from fitting the

experimental phosphorylation data of the type I showed you in the previous slide.

They made a couple of key assumptions.

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And the model is shown here the right-hand side.

And you can see that the, the patterns that

the observed in the competition model was very similar.

And this is the same graph that I took from couple of slides ago.

And so the model was able to completely

fully recapitulate what was happening, what they observed experimentally.

So this simple ODE model of just a few

reaction captures the observed circadian cycling of the phosphorylated KaiC.

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Coupled biochemical reactions can produce rhythmic oscillations

even in the absence of any network motifs.

So you, you saw that there were no.

Positive or negative feedback or feed forward loops.

It was just a coupling between a few

reactions that produced this circadian pattern of phosphorelated KaiC.

So what do we need?

What we need is appropriate rela-, yeah, relationships of interaction specificity,

such as that only series 431 as formulated.

KaiC binds KaiB and we also need appropriate rate constants

that are sufficient to produce the complex behavior.

So the rates need to be correctly tuned in this case the reaction rates are to be

quite slow because of the circadian rhythm.

And the different states that the protein needs

to be able to interact deferentially with its regulators.

So in this system, the kinetic model is not used for predictions.

However, it is still very useful in clearly proving

that the empirical observation, remember we started with this.

Observation by the counter group where they just observe that the

phosphorylation of KaiC oscillates the 24 hour cycle

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so to explain how that happens using the model tells

us that the observed behavior arises only from the measured parameters.

There are no hidden variables or mechanisms.

So the model in this case if you want tells you what you see is what you get.

So it kind of gives you a very clear view of what is going on.

Just as a note, even though this is a very simple and elegant system, this is not a

common way in which the circadian rhythms occur, mainly

circadian rhythms are much

more complicated involving transitional processes.

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The next study I would like to discuss with you.

Is, is based on PDE partial differential equation model, and it focuses

on understanding the dynamics of micro

domains of signalling components within the cell.

So cells such as neurons, epithelial cells, and others, when they stimulated

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activate a signaling molecules transiently accumulate in small sub-cellular regions.

[SOUND] And these, sub-cellular regions are called micro domains.

And the questions that often arise, are, how are these micro domains formed?

And soon as the micro domain's, meaning that the, there

is this limited area in which, the activator signaling molecular exists.

A.

It contains spacial information and, one can ask the question can the spacial

information regarding micro domains be transmitted to signaling pathways?

So here is the model in this particular cell, where its

a psychic amp pathway where a simple psychic amp pathway neurons.

And you can see that the in this model, in this pd model, cyclic ap is activated in

the two dendrites, but not not so much [UNKNOWN]

cyclic ap level do not rise in the cell body.

So, the way these models are built,

one starts off with the the biochemical parameters.

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one, one can build, rebuild a compartmental ODE model.

The compartmental ODE model is then sort of mapped onto a special model

that incorporates, we, we build these in this program called a virtual cell.

Map on to these microscopic images like the one here.

And, the various reactions of map to the various part of

the cells, and these can then, be used to run simulations.

And these simulations can produce prediction

and these predictions can be experimentally tested.

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Where for PDE models we start with experimentally constrained ODE models.

And the examples here show, are the kind of constraints that are developed.

In the top one, I think it's a steady state.

Constraint of the response curve of cyclic A and B for beta [INAUDIBLE] activation.

The experiment is on the left, the simulation is on

the right, and you can see that they match relatively closely.

Similarly, you can look at the effect of concentration.

of, active beta receptor, to activation of protein kinase, A.

And you can also look at time course experiments of a beta receptor activation.

And Map kinase increase.

So these constraints ensure that the model.

Is in a reasonable representation of the system, but remember even

when one constrains many of these reactions there's always a limitation.

These experiments and the con, constraints are

from tissue experiments and they represent sort of

average behavior of cells, while if we are doing a real spatial model we will be.

Modeling individual cells.

So their limitations to what these, experimental

constrainings were doing in making the model realistic.

But this is much better than not constraining them out.

So here is a example of, mat,

matching experiments and stimulations and, these two figures

here show experimental measurement of cyclic AMP.

This is at the basal level, this is at the

activated level, and in this case it's a loss of

image because of the fact that this particular sensor, the

[UNKNOWN] sensor for cyclic AMP the signal goes away when.

There's a, a cyclic AMP that must go up.

So one can take this image and actually sort of

import it into virtual cell and then map the reactions of the

various regions import the finite volume great and compute the

cyclic AMP production, and that is shown out her in the simulation.

And you can see that the simulations capture what is going on

in the experiment that is that the level of psychic amp increases.

This is sort of an explicit graphical comparison of the simulation and

the experiment and you can see that the future is not so bad.

Well let's not call it a failure.

The matching is not so bad.

So, the one of the first questions we asked was if cyclic AMP accumulates

in these thin dendrites, is the diameter of the dendrite.

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And elevate factor the level of cyclic AMP accumulating.

And what these simulations out here show, is and these are

called graphs where time is plotted against distance and concentration so

you can in and what this shows is that a, only when the.

Diameter is thin somewhere like at one micrometer can one observe a gradient.

As you make the diameter thicker, the gradient starts to dissipate.

Some of this was done initially by converting.

These kind of simulations were run using a time model, which

is like a ball and stick model that kind of represents